Michaelangelo, Da Vinci, Caravaggio, Botticelli, Titian, Nelli. All were once greats of the Renaissance, though if the last name on the list doesn’t ring a bell with you, you could be forgiven. Like those of her male contemporaries, Plautilla Nelli’s Biblical paintings were masterful works of beauty, but, in a tale as old as patriarchy itself, she was written out of every Renaissance history book, dismissed as just another nun with a paintbrush.

Yet, in March, almost 500 years after Nelli was born, the Uffizi in Florence is to stage its first exhibition of her work; an attempt, says the Uffizi, to begin to correct the gender imbalance that still skews every major collection in the world. As one of the world’s most influential galleries, it is making an important, if overdue, statement.

It is important to understand the impact this bias has had on the art world. These galleries, with outposts across America and Asia, are global tastemakers; championing artists, funding their work and introducing them to the world’s wealthiest collectors. It is still the case that the art that we consider to be the most valuable, in monetary but also cultural terms, is almost all by men. It is the reason that the museums in the world considered to have the greatest and strongest collections are the ones that boast works by Turner, Matisse, Van Gogh and Picasso, Pollock, Rothko, Koons, Hirst and Hockney. That a female equivalent for each of these artists doesn’t roll off the tongue says it all. It is also telling that the auction record for work by a deceased female artist is held by Georgia O’Keefe, for Jimson Weed/White Flower No1, which sold in 2014 for $44.4m; just 25% of the record-breaking $179m paid for Picasso’s Les Femmes d’Alger the following year.

Work by Louise Bourgeois in the Tate Modern Switch House. Photograph: Facundo Arrizabalaga/EPA

Yet, according to Artfinder, an online marketplace for 9,000 independent artists (a bit like a posher Etsy), women consistently outsell their male counterparts, and are the most popular picks for buyers. For every £1m worth of art made by men that is sold by the site, women sell £1.16m. In a bid to stoke debate, the company has published a report on gender equality in the art world, taking aim at the sexism of institutions higher up the pecking order.

Yet in the UK, and the international art world beyond, a shift may be occurring, driven by women who have taken the helm of some of the biggest art institutions. This year, Maria Balshaw will become the first female director of Tate Galleries, while Frances Morris, director of Tate Modern, has been consistently vocal about championing female artists since she was appointed in 2015. According to Morris, Tate Modern’s permanent collection representing 335 female artists compared with 959 male artists is “just not good enough”.

In a powerful move, she chose to devote half of the solo-artist rooms in the Tate Modern extension, Switch House, to female artists such as Louise Bourgeouis, Ana Lupas and Suzanne Lacy when it opened last summer.

“Very simply, we have made a commitment to rethinking our collection, how we build it and the choices we make,” says Morris. “And I think what we did with Switch House was in a way very simple. We didn’t dress it up as a strategy or positive discrimination – it was just great work by women and an attempt to redress the gender balance. Simple as that. And a lot of my peers said: ‘What a relief.’”

As a curator and then gallery director, Morris has been responsible for the ever-growing number of solo female shows at Tate Modern including Marlene Dumas, Sonia Delauney, Mona Hatoum and Agnes Martin. To her, the key for Tate Modern to progress towards gender parity is to untangle itself from the money-driven monster that is the art market. After all, if the major institutions continue to buy and exhibit only the blockbuster artists that currently fetch the biggest price tags at auction, then women will never get a look-in.

Morris refuses to accept that a price tag should have any bearing on what Tate Modern collects and displays. “We really have to stop celebrating creativity depending on how it’s monetised by the art market,” she says. “My heart sinks when I read things saying the Tate Modern’s collection is weak because they’re using the standards of the last auction sales or Moma in New York. That’s not what we’re about. It’s not about constructing a collection based on shopping and taste in the private sector. We’re interested in art whose value lies in excellence and provocation and fascination for the public. And, more often than not, that art is made by women.”

In the public sphere, Morris is certainly not acting alone. Iwona Blazwick, the director of Whitechapel Gallery, has staged more solo shows by women than men in recent years, including a current exhibition by Guerilla Girls, the artist-activist group set up in the 1980s to challenge the dismal representation of women in the art world.

“It is still the case that very few women can make a living out of being a full-time artist,” says Blazwick. “They are increasing in number, there are some very prominent female artists, but it has been a long, hard struggle. But I would also say that things are changing, and this chicken-or-egg cycle is being broken at last.”

The issue has also been championed by Hans Ulrich Obrist, the director of the Serpentine Gallery who was last year named the most powerful figure in the art world. “I always ask if there is a pioneering or exciting female artist who needs rediscovering,” he says of his curating methodology. “That’s how I found out about the work of great Brazilian artist, Lygia Pape, about Phyllida Barlow and, in the Middle East, Etel Adnan.” All have since had solo shows at some of the most important galleries around the world.

Whether commercial galleries are having a moment of reckoning is up for debate. Susan May, the artistic director of White Cube, admits that “gender imbalance across the art world is an issue that we are conscious of and acknowledge that we should all find ways to do better”; the gallery will be announcing forthcoming solo shows with four female artists and a group show of 30 female surrealists.

Elsewhere, Hauser and Wirth chose to open their new LA gallery last year with an exhibition of female abstract sculpture, while Lisson Gallery opened its first New York gallery in May with a show by female Cuban artist Carmen Herrera, who for years had worked in relative obscurity. “Carmen is the perfect example of an artist who was part of that abstract movement, along with Ellsworth Kelly and Barnett Newman, but was completely overlooked,” says Gifford-Mead. “So the chance to work with her, especially while she’s still alive, and correct some of those wrongs, has been really good for us.”

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In 2017, just over half of the artists Lisson is showing will be female. “We knew the disparity was there – we just didn’t know it was quite so stark. Within the gallery over the last year, it’s something we’ve taken note of and something that we’re working really hard to correct properly and quickly.”

The big auction houses, which equal commercial galleries in terms of influence, also appear to be making an effort. This month, Sotheby’s will open a joint show by Louise Bourgeois and Yayoi Kusama, two 20th-century female artists whose works command millions at auction, making them rarities in the field.

For the few galleries that have been defiantly fighting the corner for female artists for years, the fact that the art world is finally catching up is bound to be a relief. Jane Hamlyn, who runs Frith Street Gallery, for example, has spent decades ruthlessly championing artists such as Marlene Dumas, Cornelia Parker and Fiona Banner.

A work by Yayoi Kusama, in the Tate Modern’s Switch House extension. Photograph: Daniel Leal-Olivas/AFP/Getty Images

How fast irreversible change will come is hard to predict. UK public galleries face difficult financial straits ahead, and the increasing reliance on private and commercial funding could ensure gender parity is less of a priority in the future. Debate, too, continues to rage around how best to go back and fill in the gaps in our historic art collections currently lacking women – can female artists simply be “reinserted” into art history?

For the time being, however, the real, seismic changes are happening not in the big global institutions but the smaller independent and commercial galleries. Here a new generation of female artists – many of whom work across online, video and virtual spheres that are very difficult for the traditional “physical” art market to grasp – finally have a platform where they aren’t considered to be a risky investment.